2019 AMC 10C Problems/Problem 22
chicks are sitting in a circle. The first chick in the circle says the number , then the chick seats away from the first chick says the number , then the chick seats away from the chicken that said the number says the number , and so on. The process will always go clockwise. Some of the chicks in the circle will say more than one number while others might not even say a number at all. The process stops when the th number is said. How many numbers would the chick that said have said by that point (including )?
The number is said by chick . Note that when , the first chick said the number. Thus, we are looking for , or . This is equivalent to stating that and . It is clear that there are numbers that the first chick says every numbers said by all chicks, so our answer is